Evolutionary Biology | VOL. 49
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Dimensions of Morphological Integration

Publication Date Aug 4, 2022

Abstract

Over several generations of evolutionary and developmental biologists, ever since Olson and Miller\u2019s pioneering work of the 1950\u2019s, the concept of \u201cmorphological integration\u201d as applied to Gaussian representations N(mu ,Sigma ) of morphometric data has been a focus equally of methodological innovation and methodological perplexity. Reanalysis of a century-old example from Sewall Wright shows how some fallacies of distance analysis by correlations can be avoided by careful matching of the distance rosters involved to a different multivariate approach, factor analysis. I reinterpret his example by restoring the information (means and variances) ignored by the correlation matrix, while confirming what Wright called \u201cspecial size factors\u201d by a different technique, inspection of the concentration matrix Sigma ^{-1}. In geometric morphometrics (GMM), data accrue instead as Cartesian coordinates of labelled points; nevertheless, just as in the Wright example, statistical manipulations do better when they reconsider the normalizations that went into the generation of those coordinates. Here information about both mu and Sigma , the means and the variances/covariances, can be preserved via the Boas coordinates (Procrustes shape coordinates without the size adjustment) that protect the role of size per se as an essential explanatory factor while permitting the analyst to acknowledge the realities of animal anatomy and its trajectories over time or size in the course of an analysis. A descriptive quantity...

Concepts

Procrustes Shape Coordinates Geometric Morphometrics Statistical Manipulations Size Adjustment Loadings Of Principal Component Multivariate Approach Correlation Matrix Statistical Guidance Developmental Biologists Point Of View

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